I don't think it's wrong not to apologize when you don't mean it, but my opinion is just that... I think everyone gets to make up their own mind what is acceptable behavior for them.

That said, you may not feel it is appropriate to apologize for getting angry - I know I don't, anger is part of the human experience; you might find it acceptable to apologize for things that you said or did while angry. In my opinion, anger is okay, beating people up with that anger is not okay and so, I will not apologize for my anger but I might apologize for something I did while I was angry.

If you can't apologize for that it's probably because you meant everything you said or did, which might mean that you don't like him very much and he's not all that good a fit for you.